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  4. Two kg of a monoatomic gas is at a pressure of 4 × 104 N/m2 . The density of the gas is 8 kg /m3. What is the order of energy of the gas due to its thermal motion ?

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Q. Two kg of a monoatomic gas is at a pressure of $4 \times 10^4 \; N/m^2$ . The density of the gas is $8 \; kg /m^3$. What is the order of energy of the gas due to its thermal motion ?

JEE MainJEE Main 2019Kinetic Theory

Solution:

Thermal energy of N molecule
$ = N\left(\frac{3}{2}kT\right) $
$ =\frac{N}{N_{A}} \frac{3}{2}RT $
$ = \frac{3}{2}\left(nRT\right) $
$ =\frac{3}{2}PV $
$=\frac{3}{2}P\left(\frac{m}{8}\right)$
$ = \frac{3}{2} \times4\times10^{4} \times\frac{2}{8} $
$ =1.5 \times10^{4} $
order will $10^4$